Yes, as Dale says, the same protections apply to the premises of consulates and embassies. Under the Vienna Conventions, local authorities need the permission of the head-of-mission to enter the premises of either. However, "premises" are defined differently for embassies and consulates: the "premises" of an embassy includes more than the "premises" of a consulate, so more of the embassy is protected than of the consulate.
What protection do the premises of embassies and consulates get?
Embassies are covered by the 1961 Vienna Convention on Diplomatic Relations. Article 22 of that Convention says:
"The premises of the mission shall be inviolable. The agents of the receiving State may not enter them, except with the consent of the head of the mission."
Consulates are covered by the 1963 Vienna Convention on Consular Relations. Article 31 of that Convention, on the Inviolability of the consular premises says:
"Consular premises shall be inviolable to the extent provided in this article. The authorities of the receiving State shall not enter that part of the consular premises which is used exclusively for the purpose of the work of the consular post except with the consent of the head of the consular post..."
What exactly is protected?
As mentioned above, the definition of "premises" given in the two conventions are not the same.
The premises of embassies include all land and buildings
"used for the purposes of the mission including the residence of the head of the mission."
The premises of consulates however, include all land and building
"used exclusively for the purposes of the consular post."
So, at the very least, the difference is that consular residences, even if they are within the consulate, are not covered. (From the report of the working group that drafted the consular rules, it appears they did not include residences because those residences were not general protected under earlier treaties or laws.)